where \(|p|= v_o^{2/3} a^2,\; \kappa = 8\pi G/c^4\) , \(v_o\)  denotes the volume of the fiducial cell measured by \(\mathring{q}_{ab}\) ,
\(\mathring{q}\)  is the determinant of \(\mathring{q}_{ab}\) , and \(\gamma \)  is the Barbero-Immirzi parameter whose value can be set to \(\gamma \approx 0.2375\)  using black hole thermodynamics in LQG [1]}. For classical solutions, symmetry reduced connection \(c\)  is related to time derivative of scale factor as \(c = \gamma \dot{a}\) , where an over dot denotes a derivative with respect to \(t\)  for the choice \(N = 1\) ,.
